Explanatory Model Building
1 MVP
We’ve looked at a few different ways in which we can build models this week, including how to prepare them properly. This weekend we’ll build a multiple linear regression model on a dataset which will need some preparation. The data can be found in the data folder, along with a data dictionary
We want to investigate the avocado dataset, and, in particular, to model the AveragePrice of the avocados. Use the tools we’ve worked with this week in order to prepare your dataset and find appropriate predictors. Once you’ve built your model use the validation techniques discussed on Wednesday to evaluate it. Feel free to focus either on building an explanatory or a predictive model, or both if you are feeling energetic!
As part of the MVP we want you not to just run the code but also have a go at interpreting the results and write your thinking in comments in your script.
Hints and tips
regionmay lead to many dummy variables. Think carefully about whether to include this variable or not (there is no one ‘right’ answer to this!)- Think about whether each variable is categorical or numerical. If categorical, make sure that the variable is represented as a factor.
- We will not treat this data as a time series, so
Datewill not be needed in your models, but can you extract any useful features out ofDatebefore you discard it? - If you want to build a predictive model, consider using either
leapsorglmultito help with this.
1.1 Researching and prearing our data
Here is what we found looking for information on the ‘avocado’ data. I am accepting this info as reliable.
“The table represents weekly retail scan data for National retail volume (units) and price. Retail scan data comes directly from retailers’ cash registers based on actual retail sales of Hass avocados. Starting in 2013, the table below reflects an expanded, multi-outlet retail data set. Multi-outlet reporting includes an aggregation of the following channels: grocery, mass, club, drug, dollar and military. The Average Price (of avocados) in the table reflects a per unit (per avocado) cost, even when multiple units (avocados) are sold in bags. The Product Lookup codes (PLU’s) in the table are only for Hass avocados. Other varieties of avocados (e.g. greenskins) are not included in this table.”
Relevant info for understanding ‘obscure’ variable names:
AveragePrice - the average price of a single avocado Region - the city or region of the observation, i.e. where avocados were sold. Total Volume - Total number of avocados sold 4046 - Total number of small avocados sold (PLU 4046) 4225 - Total number of medium avocados sold (PLU 4225) 4770 - Total number of large avocados sold (PLU 4770)
Apparently average price recorded here is not related to bag size so we can drop these variables. Also region doesn’t seem to have a direct relation with average price so it may be safe and beneficial to drop it too.
the x1 variable records the week in which sales were recorded in a 52 weeks per year format. Although our brief is not interested in time series and forecasting we can investigate if seasonality has an impact on average price. Avocados are very sensitive to variations in temperature so weather patterns may impact production and potentially prices. We have decided to keep only data for years 2015 - 2017 dropping partial 2018 data. This could help especially if seasons play some role on average price.
So, we’ll focus on ‘average price,’‘type’ and ‘total volume’. We’ll use ‘x1, ’date’ and ‘year’ to engineer variables which will enable us to explore seasonality.
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.4 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.0## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(janitor)##
## Attaching package: 'janitor'## The following objects are masked from 'package:stats':
##
## chisq.test, fisher.testlibrary(ggfortify)
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(modelr)1.1.1 cleaning var names and subsetting
avocado_df_exp <- read_csv("data/avocado.csv") %>%
clean_names() %>%
select(x1:x4770, type:year) %>%
rename(week = "x1",
small = "x4046",
medium = "x4225",
large = "x4770") %>%
filter(date <= "2017-12-31")## Warning: Missing column names filled in: 'X1' [1]##
## -- Column specification --------------------------------------------------------
## cols(
## X1 = col_double(),
## Date = col_date(format = ""),
## AveragePrice = col_double(),
## `Total Volume` = col_double(),
## `4046` = col_double(),
## `4225` = col_double(),
## `4770` = col_double(),
## `Total Bags` = col_double(),
## `Small Bags` = col_double(),
## `Large Bags` = col_double(),
## `XLarge Bags` = col_double(),
## type = col_character(),
## year = col_double(),
## region = col_character()
## )avocado_tidy <- avocado_df_exp %>%
mutate(month = as.character(month(date))) %>%
mutate(season = case_when(
month == "12" | month == "1" | month == "2" ~ "winter",
month == "3" | month == "4" | month == "5" ~ "spring",
month == "6" | month == "7" | month == "8" ~ "summer",
month == "9" | month == "10" | month == "11" ~ "autumn")
) %>%
mutate(type = as.factor(type)) %>%
mutate(season = as.factor(season)) %>%
mutate(year = as.factor(year)) %>%
#mutate(week = as.factor(week))
select(-date)We suspect ‘total volume’ to be strongly correlated to avocado sizes so we test and if so drop avocado sizes.
avocado_tidy %>%
select(total_volume:large) %>%
ggpairs()
avocado_tidy <- avocado_tidy %>%
select(-c(small, medium, large))Let’s look at summary statistics
summary(avocado_tidy)## week average_price total_volume type
## Min. : 0.00 Min. :0.44 Min. : 85 conventional:8478
## 1st Qu.:13.00 1st Qu.:1.10 1st Qu.: 10460 organic :8475
## Median :26.00 Median :1.37 Median : 104849
## Mean :25.66 Mean :1.41 Mean : 834110
## 3rd Qu.:39.00 3rd Qu.:1.67 3rd Qu.: 423186
## Max. :52.00 Max. :3.25 Max. :61034457
## year month season
## 2015:5615 Length:16953 autumn:4212
## 2016:5616 Class :character spring:4320
## 2017:5722 Mode :character summer:4210
## winter:4211
##
## total volume is extremely skewed so this will affect our models. We need to look into this.
total_vol_by_type <- avocado_tidy %>%
group_by(type) %>%
summarise(avg_total_vol= mean(total_volume)) %>%
mutate(pct = prop.table(avg_total_vol) * 100)## `summarise()` ungrouping output (override with `.groups` argument)total_vol_by_typeMore than 97 % of avocados in the data is conventional. It makes sense to focus on this type for average price modelling
avocado_tidy_conv <- avocado_tidy %>%
filter(type == "conventional") %>%
select(-type)
avocado_tidy_org <- avocado_tidy %>%
filter(type == "organic") %>%
select(-type)1.2 Visualising our data
both_types <- ggplot(avocado_tidy) +
aes(x = total_volume, y = average_price) +
geom_point(size = 1L, colour = "#0c4c8a") +
geom_smooth(span = 0.75) +
scale_x_continuous(trans = "log") +
scale_y_continuous(trans = "log") +
labs(title = "Average price decreases when Total Volume increseas") +
theme_minimal()
conventional <- ggplot(avocado_tidy_conv) +
aes(x = total_volume, y = average_price) +
geom_point(size = 1L, colour = "#0c4c8a") +
geom_smooth(span = 0.75) +
scale_x_continuous(trans = "log") +
scale_y_continuous(trans = "log") +
labs(title = "Average price decreases when Total Volume increseas") +
theme_minimal()
organic <- ggplot(avocado_tidy_org) +
aes(x = total_volume, y = average_price) +
geom_point(size = 1L, colour = "#0c4c8a") +
geom_smooth(span = 0.75) +
scale_x_continuous(trans = "log") +
scale_y_continuous(trans = "log") +
labs(title = "Average price decreases when Total Volume increseas") +
theme_minimal()
both_types## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
conventional## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
organic## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
ggplot(avocado_df_exp) +
aes(x = date, y = average_price, colour = type) +
geom_line(size = 1L) +
scale_color_hue() +
labs(title = "Average Price has a certain degree of seasonality") +
theme_minimal() +
facet_wrap(vars(type))
ggplot(avocado_df_exp) +
aes(x = type, y = average_price, fill = type) +
geom_boxplot() +
scale_fill_hue() +
labs(title = "As expected average price is higher for organic type") +
theme_minimal()
ggplot(avocado_df_exp) +
aes(x = date, weight = total_volume) +
geom_bar(fill = "#0c4c8a") +
labs(title = "Total Volume has also a pattern of seasonality") +
theme_minimal()
1.3 Model development
1.3.1 First Predictor - type
avocado_tidy %>%
ggpairs(aes(colour = type, alpha = 0.5))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
avocado_tidy %>%
ggpairs(aes(colour = season, alpha = 0.5))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3.1.1 average price + type
mod_type <- lm(log(average_price) ~ type, data = avocado_tidy)
mod_type##
## Call:
## lm(formula = log(average_price) ~ type, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic
## 0.1222 0.3591summary(mod_type)##
## Call:
## lm(formula = log(average_price) ~ type, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.30232 -0.13775 0.00724 0.15524 0.69732
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.122230 0.002517 48.57 <2e-16 ***
## typeorganic 0.359108 0.003559 100.89 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2317 on 16951 degrees of freedom
## Multiple R-squared: 0.3752, Adjusted R-squared: 0.3752
## F-statistic: 1.018e+04 on 1 and 16951 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type)
1.3.1.2 average price + total volume
mod_total_volume <- lm(average_price ~ log(total_volume), data = avocado_tidy)
mod_total_volume##
## Call:
## lm(formula = average_price ~ log(total_volume), data = avocado_tidy)
##
## Coefficients:
## (Intercept) log(total_volume)
## 2.5746 -0.1032summary(mod_total_volume)##
## Call:
## lm(formula = average_price ~ log(total_volume), data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.06658 -0.23668 -0.03644 0.19778 1.67839
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.574617 0.012777 201.50 <2e-16 ***
## log(total_volume) -0.103156 0.001109 -92.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3327 on 16951 degrees of freedom
## Multiple R-squared: 0.3378, Adjusted R-squared: 0.3378
## F-statistic: 8647 on 1 and 16951 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_total_volume)
1.3.1.3 average price + month
mod_month <- lm(average_price ~ month, data = avocado_tidy)
mod_month##
## Call:
## lm(formula = average_price ~ month, data = avocado_tidy)
##
## Coefficients:
## (Intercept) month10 month11 month12 month2 month3
## 1.28919 0.29050 0.16638 0.04193 -0.02957 0.04178
## month4 month5 month6 month7 month8 month9
## 0.08519 0.05741 0.11978 0.17289 0.22333 0.28347summary(mod_month)##
## Call:
## lm(formula = average_price ~ month, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.99265 -0.30265 -0.03265 0.25444 1.79562
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.28919 0.01018 126.589 < 2e-16 ***
## month10 0.29050 0.01440 20.170 < 2e-16 ***
## month11 0.16638 0.01468 11.336 < 2e-16 ***
## month12 0.04193 0.01468 2.856 0.00429 **
## month2 -0.02957 0.01499 -1.973 0.04854 *
## month3 0.04178 0.01468 2.846 0.00443 **
## month4 0.08519 0.01468 5.805 6.56e-09 ***
## month5 0.05741 0.01440 3.986 6.74e-05 ***
## month6 0.11978 0.01500 7.987 1.47e-15 ***
## month7 0.17289 0.01440 12.004 < 2e-16 ***
## month8 0.22333 0.01468 15.216 < 2e-16 ***
## month9 0.28347 0.01499 18.910 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.396 on 16941 degrees of freedom
## Multiple R-squared: 0.06224, Adjusted R-squared: 0.06163
## F-statistic: 102.2 on 11 and 16941 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_month)
1.3.1.4 average price + week
mod_week <- lm(average_price ~ week, data = avocado_tidy)
mod_week##
## Call:
## lm(formula = average_price ~ week, data = avocado_tidy)
##
## Coefficients:
## (Intercept) week
## 1.521376 -0.004322summary(mod_week)##
## Call:
## lm(formula = average_price ~ week, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.03138 -0.30958 -0.03357 0.25855 1.80855
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.5213759 0.0061104 248.98 <2e-16 ***
## week -0.0043223 0.0002052 -21.07 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4036 on 16951 degrees of freedom
## Multiple R-squared: 0.02551, Adjusted R-squared: 0.02545
## F-statistic: 443.8 on 1 and 16951 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_week)
1.3.1.5 average price + season
mod_season <- lm(average_price ~ season, data = avocado_tidy)
mod_season##
## Call:
## lm(formula = average_price ~ season, data = avocado_tidy)
##
## Coefficients:
## (Intercept) seasonspring seasonsummer seasonwinter
## 1.53615 -0.18560 -0.07357 -0.24209summary(mod_season)##
## Call:
## lm(formula = average_price ~ season, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.95615 -0.30405 -0.03257 0.25595 1.81945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.536147 0.006130 250.602 <2e-16 ***
## seasonspring -0.185600 0.008615 -21.545 <2e-16 ***
## seasonsummer -0.073574 0.008670 -8.486 <2e-16 ***
## seasonwinter -0.242093 0.008669 -27.925 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3978 on 16949 degrees of freedom
## Multiple R-squared: 0.05314, Adjusted R-squared: 0.05297
## F-statistic: 317.1 on 3 and 16949 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_season)
1.3.1.6 average price + year
mod_year <- lm(average_price ~ year, data = avocado_tidy)
mod_year##
## Call:
## lm(formula = average_price ~ year, data = avocado_tidy)
##
## Coefficients:
## (Intercept) year2016 year2017
## 1.37559 -0.03695 0.13954summary(mod_year)##
## Call:
## lm(formula = average_price ~ year, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.07513 -0.29864 -0.03864 0.25487 1.91136
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.375590 0.005360 256.632 < 2e-16 ***
## year2016 -0.036951 0.007580 -4.875 1.1e-06 ***
## year2017 0.139537 0.007545 18.494 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4017 on 16950 degrees of freedom
## Multiple R-squared: 0.03476, Adjusted R-squared: 0.03465
## F-statistic: 305.2 on 2 and 16950 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_year)
1.3.2 Second Predictor - month
remaining_resid <- avocado_tidy %>%
add_residuals(mod_type) %>%
select(-c(average_price, type))remaining_resid %>%
ggpairs(aes(colour = season, alpha = 0.5))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3.2.1 avg_p + type + week
mod_type_week <- lm(average_price ~ type + week, data = avocado_tidy)
mod_type_week##
## Call:
## lm(formula = average_price ~ type + week, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic week
## 1.271166 0.500254 -0.004317summary(mod_type_week)##
## Call:
## lm(formula = average_price ~ type + week, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.14577 -0.20821 -0.02663 0.19131 1.55832
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.271166 0.005377 236.40 <2e-16 ***
## typeorganic 0.500254 0.004865 102.83 <2e-16 ***
## week -0.004317 0.000161 -26.81 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3167 on 16950 degrees of freedom
## Multiple R-squared: 0.3999, Adjusted R-squared: 0.3998
## F-statistic: 5648 on 2 and 16950 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_week)
1.3.2.2 avg_p + type + total volume
mod_type_total_volume <- lm(average_price ~ type + log(total_volume), data = avocado_tidy)
mod_type_total_volume##
## Call:
## lm(formula = average_price ~ type + log(total_volume), data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic log(total_volume)
## 1.75552 0.33349 -0.04535summary(mod_type_total_volume)##
## Call:
## lm(formula = average_price ~ type + log(total_volume), data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.14711 -0.20784 -0.02665 0.18296 1.60193
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.755519 0.023313 75.30 <2e-16 ***
## typeorganic 0.333487 0.008093 41.21 <2e-16 ***
## log(total_volume) -0.045349 0.001757 -25.81 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3172 on 16950 degrees of freedom
## Multiple R-squared: 0.3981, Adjusted R-squared: 0.398
## F-statistic: 5606 on 2 and 16950 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_total_volume)
1.3.2.3 avg_p + type + year
mod_type_year <- lm(average_price ~ type + year, data = avocado_tidy)
mod_type_year##
## Call:
## lm(formula = average_price ~ type + year, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic year2016 year2017
## 1.1255 0.5003 -0.0370 0.1396summary(mod_type_year)##
## Call:
## lm(formula = average_price ~ type + year, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.32537 -0.18880 -0.01548 0.18463 1.66120
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.125478 0.004838 232.624 < 2e-16 ***
## typeorganic 0.500313 0.004827 103.653 < 2e-16 ***
## year2016 -0.036995 0.005930 -6.238 4.53e-10 ***
## year2017 0.139580 0.005903 23.647 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3142 on 16949 degrees of freedom
## Multiple R-squared: 0.4092, Adjusted R-squared: 0.4091
## F-statistic: 3914 on 3 and 16949 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_year)
1.3.2.4 avg_p + type + month
mod_type_month <- lm(average_price ~ type + month, data = avocado_tidy)
mod_type_month##
## Call:
## lm(formula = average_price ~ type + month, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12 month2
## 1.03904 0.50028 0.29050 0.16638 0.04210 -0.02957
## month3 month4 month5 month6 month7 month8
## 0.04178 0.08519 0.05741 0.12016 0.17289 0.22333
## month9
## 0.28347summary(mod_type_month)##
## Call:
## lm(formula = average_price ~ type + month, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.14982 -0.20115 -0.02194 0.19046 1.54548
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.039045 0.008238 126.129 < 2e-16 ***
## typeorganic 0.500283 0.004715 106.112 < 2e-16 ***
## month10 0.290496 0.011163 26.023 < 2e-16 ***
## month11 0.166376 0.011376 14.626 < 2e-16 ***
## month12 0.042104 0.011378 3.701 0.000216 ***
## month2 -0.029572 0.011619 -2.545 0.010930 *
## month3 0.041775 0.011376 3.672 0.000241 ***
## month4 0.085194 0.011376 7.489 7.27e-14 ***
## month5 0.057414 0.011163 5.143 2.73e-07 ***
## month6 0.120165 0.011624 10.338 < 2e-16 ***
## month7 0.172890 0.011163 15.488 < 2e-16 ***
## month8 0.223328 0.011376 19.632 < 2e-16 ***
## month9 0.283468 0.011619 24.397 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3069 on 16940 degrees of freedom
## Multiple R-squared: 0.4367, Adjusted R-squared: 0.4363
## F-statistic: 1094 on 12 and 16940 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month)
1.3.2.4.1 running avova() to confirm ‘month’
anova(mod_type, mod_type_month)## Warning in anova.lmlist(object, ...): models with response '"average_price"'
## removed because response differs from model 11.3.2.5 avg_p + type + season
mod_type_season <- lm(average_price ~ type + season, data = avocado_tidy)
mod_type_season##
## Call:
## lm(formula = average_price ~ type + season, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic seasonspring seasonsummer seasonwinter
## 1.28600 0.50029 -0.18560 -0.07346 -0.24203summary(mod_type_season)##
## Call:
## lm(formula = average_price ~ type + season, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.16069 -0.20284 -0.02284 0.18931 1.56931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.286001 0.005325 241.48 <2e-16 ***
## typeorganic 0.500291 0.004751 105.29 <2e-16 ***
## seasonspring -0.185600 0.006698 -27.71 <2e-16 ***
## seasonsummer -0.073455 0.006741 -10.90 <2e-16 ***
## seasonwinter -0.242034 0.006741 -35.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3093 on 16948 degrees of freedom
## Multiple R-squared: 0.4276, Adjusted R-squared: 0.4274
## F-statistic: 3165 on 4 and 16948 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_season)
1.3.3 Third Predictor - year
remaining_resid <- avocado_tidy %>%
add_residuals(mod_month) %>%
select(-c(average_price, type, month))remaining_resid %>%
ggpairs(aes(colour = season, alpha = 0.5))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3.3.1 avg_p + type + month + total volume
mod_type_month_total_volume <- lm(average_price ~ type + month + log(total_volume), data = avocado_tidy)
mod_type_month_total_volume##
## Call:
## lm(formula = average_price ~ type + month + log(total_volume),
## data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11
## 1.60846 0.34000 0.28755 0.16171
## month12 month2 month3 month4
## 0.04255 -0.02532 0.04463 0.09181
## month5 month6 month7 month8
## 0.06661 0.12723 0.17821 0.22518
## month9 log(total_volume)
## 0.28350 -0.04358summary(mod_type_month_total_volume)##
## Call:
## lm(formula = average_price ~ type + month + log(total_volume),
## data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.13248 -0.19748 -0.01783 0.17872 1.47888
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.608457 0.023279 69.096 < 2e-16 ***
## typeorganic 0.340002 0.007690 44.213 < 2e-16 ***
## month10 0.287554 0.010946 26.269 < 2e-16 ***
## month11 0.161713 0.011156 14.496 < 2e-16 ***
## month12 0.042553 0.011156 3.814 0.000137 ***
## month2 -0.025317 0.011394 -2.222 0.026299 *
## month3 0.044628 0.011155 4.001 6.34e-05 ***
## month4 0.091807 0.011157 8.228 < 2e-16 ***
## month5 0.066609 0.010951 6.082 1.21e-09 ***
## month6 0.127226 0.011401 11.160 < 2e-16 ***
## month7 0.178207 0.010948 16.278 < 2e-16 ***
## month8 0.225184 0.011154 20.188 < 2e-16 ***
## month9 0.283504 0.011393 24.885 < 2e-16 ***
## log(total_volume) -0.043575 0.001671 -26.081 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.301 on 16939 degrees of freedom
## Multiple R-squared: 0.4584, Adjusted R-squared: 0.458
## F-statistic: 1103 on 13 and 16939 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_total_volume)
1.3.3.2 avg_p + type + month + season
mod_type_month_season <- lm(average_price ~ type + month + season, data = avocado_tidy)
mod_type_month_season##
## Call:
## lm(formula = average_price ~ type + month + season, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12
## 1.03904 0.50028 0.29050 0.16638 0.04210
## month2 month3 month4 month5 month6
## -0.02957 0.04178 0.08519 0.05741 0.12016
## month7 month8 month9 seasonspring seasonsummer
## 0.17289 0.22333 0.28347 NA NA
## seasonwinter
## NAsummary(mod_type_month_season)##
## Call:
## lm(formula = average_price ~ type + month + season, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.14982 -0.20115 -0.02194 0.19046 1.54548
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.039045 0.008238 126.129 < 2e-16 ***
## typeorganic 0.500283 0.004715 106.112 < 2e-16 ***
## month10 0.290496 0.011163 26.023 < 2e-16 ***
## month11 0.166376 0.011376 14.626 < 2e-16 ***
## month12 0.042104 0.011378 3.701 0.000216 ***
## month2 -0.029572 0.011619 -2.545 0.010930 *
## month3 0.041775 0.011376 3.672 0.000241 ***
## month4 0.085194 0.011376 7.489 7.27e-14 ***
## month5 0.057414 0.011163 5.143 2.73e-07 ***
## month6 0.120165 0.011624 10.338 < 2e-16 ***
## month7 0.172890 0.011163 15.488 < 2e-16 ***
## month8 0.223328 0.011376 19.632 < 2e-16 ***
## month9 0.283468 0.011619 24.397 < 2e-16 ***
## seasonspring NA NA NA NA
## seasonsummer NA NA NA NA
## seasonwinter NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3069 on 16940 degrees of freedom
## Multiple R-squared: 0.4367, Adjusted R-squared: 0.4363
## F-statistic: 1094 on 12 and 16940 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_season)
1.3.3.3 avg_p + type + month + year
mod_type_month_year <- lm(average_price ~ type + month + year, data = avocado_tidy)
mod_type_month_year##
## Call:
## lm(formula = average_price ~ type + month + year, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12 month2
## 1.00211 0.50030 0.29050 0.17149 0.03636 -0.02711
## month3 month4 month5 month6 month7 month8
## 0.04689 0.07948 0.06746 0.12279 0.17289 0.22844
## month9 year2016 year2017
## 0.28593 -0.03730 0.14070summary(mod_type_month_year)##
## Call:
## lm(formula = average_price ~ type + month + year, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.25000 -0.18917 -0.01311 0.18043 1.49439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.002107 0.008701 115.174 < 2e-16 ***
## typeorganic 0.500303 0.004565 109.594 < 2e-16 ***
## month10 0.290496 0.010809 26.876 < 2e-16 ***
## month11 0.171489 0.011025 15.554 < 2e-16 ***
## month12 0.036364 0.011019 3.300 0.000969 ***
## month2 -0.027110 0.011253 -2.409 0.015996 *
## month3 0.046888 0.011025 4.253 2.12e-05 ***
## month4 0.079484 0.011017 7.214 5.65e-13 ***
## month5 0.067464 0.010816 6.237 4.56e-10 ***
## month6 0.122791 0.011257 10.908 < 2e-16 ***
## month7 0.172890 0.010809 15.995 < 2e-16 ***
## month8 0.228441 0.011025 20.720 < 2e-16 ***
## month9 0.285930 0.011253 25.410 < 2e-16 ***
## year2016 -0.037298 0.005621 -6.636 3.32e-11 ***
## year2017 0.140698 0.005600 25.122 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2972 on 16938 degrees of freedom
## Multiple R-squared: 0.4719, Adjusted R-squared: 0.4715
## F-statistic: 1081 on 14 and 16938 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_year)
1.3.4 Forth Predictor - total volume
remaining_resid <- avocado_tidy %>%
add_residuals(mod_year) %>%
select(-c(average_price, type, month, year))remaining_resid %>%
ggpairs(aes(colour = season, alpha = 0.5))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3.4.1 avg_p + type + month + year + total volume
mod_type_month_year_total_volume <- lm(average_price ~ type + month + year + total_volume, data = avocado_tidy)
mod_type_month_year_total_volume##
## Call:
## lm(formula = average_price ~ type + month + year + total_volume,
## data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12
## 1.011e+00 4.912e-01 2.894e-01 1.704e-01 3.578e-02
## month2 month3 month4 month5 month6
## -2.653e-02 4.667e-02 7.951e-02 6.805e-02 1.231e-01
## month7 month8 month9 year2016 year2017
## 1.728e-01 2.281e-01 2.852e-01 -3.686e-02 1.412e-01
## total_volume
## -5.769e-09summary(mod_type_month_year_total_volume)##
## Call:
## lm(formula = average_price ~ type + month + year + total_volume,
## data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.25008 -0.18825 -0.01059 0.17964 1.49500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.011e+00 8.755e-03 115.526 < 2e-16 ***
## typeorganic 4.912e-01 4.685e-03 104.844 < 2e-16 ***
## month10 2.894e-01 1.079e-02 26.822 < 2e-16 ***
## month11 1.704e-01 1.100e-02 15.485 < 2e-16 ***
## month12 3.578e-02 1.100e-02 3.253 0.00114 **
## month2 -2.653e-02 1.123e-02 -2.362 0.01817 *
## month3 4.667e-02 1.100e-02 4.242 2.23e-05 ***
## month4 7.951e-02 1.100e-02 7.231 4.99e-13 ***
## month5 6.805e-02 1.079e-02 6.304 2.98e-10 ***
## month6 1.231e-01 1.123e-02 10.957 < 2e-16 ***
## month7 1.728e-01 1.079e-02 16.018 < 2e-16 ***
## month8 2.281e-01 1.100e-02 20.727 < 2e-16 ***
## month9 2.852e-01 1.123e-02 25.399 < 2e-16 ***
## year2016 -3.686e-02 5.610e-03 -6.571 5.15e-11 ***
## year2017 1.412e-01 5.590e-03 25.257 < 2e-16 ***
## total_volume -5.769e-09 6.932e-10 -8.323 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2966 on 16937 degrees of freedom
## Multiple R-squared: 0.4741, Adjusted R-squared: 0.4736
## F-statistic: 1018 on 15 and 16937 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_year_total_volume)
1.3.4.2 avg_p + type + month + year + week
mod_type_month_year_week <- lm(average_price ~ type + month + year + week, data = avocado_tidy)
mod_type_month_year_week##
## Call:
## lm(formula = average_price ~ type + month + year + week, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12 month2
## 1.398290 0.500213 -0.022093 -0.177098 -0.347067 -0.061808
## month3 month4 month5 month6 month7 month8
## -0.021168 -0.023442 -0.071366 -0.050825 -0.035485 -0.015932
## month9 year2016 year2017 week
## 0.008115 -0.039921 0.145008 -0.008016summary(mod_type_month_year_week)##
## Call:
## lm(formula = average_price ~ type + month + year + week, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.23763 -0.18814 -0.01214 0.18029 1.49463
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.398290 0.089820 15.568 < 2e-16 ***
## typeorganic 0.500213 0.004563 109.633 < 2e-16 ***
## month10 -0.022093 0.071357 -0.310 0.7569
## month11 -0.177098 0.079426 -2.230 0.0258 *
## month12 -0.347067 0.087218 -3.979 6.94e-05 ***
## month2 -0.061808 0.013703 -4.510 6.51e-06 ***
## month3 -0.021168 0.018901 -1.120 0.2628
## month4 -0.023442 0.025703 -0.912 0.3618
## month5 -0.071366 0.033139 -2.154 0.0313 *
## month6 -0.050825 0.040759 -1.247 0.2124
## month7 -0.035485 0.048244 -0.736 0.4620
## month8 -0.015932 0.056232 -0.283 0.7769
## month9 0.008115 0.063689 0.127 0.8986
## year2016 -0.039921 0.005649 -7.067 1.64e-12 ***
## year2017 0.145008 0.005681 25.524 < 2e-16 ***
## week -0.008016 0.001809 -4.432 9.41e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.297 on 16937 degrees of freedom
## Multiple R-squared: 0.4725, Adjusted R-squared: 0.4721
## F-statistic: 1012 on 15 and 16937 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_year_week)
1.3.4.3 avg_p + type + month + year + season
mod_type_month_year_season <- lm(average_price ~ type + month + year + season, data = avocado_tidy)
mod_type_month_year_season##
## Call:
## lm(formula = average_price ~ type + month + year + season, data = avocado_tidy)
##
## Coefficients:
## (Intercept) typeorganic month10 month11 month12
## 1.00211 0.50030 0.29050 0.17149 0.03636
## month2 month3 month4 month5 month6
## -0.02711 0.04689 0.07948 0.06746 0.12279
## month7 month8 month9 year2016 year2017
## 0.17289 0.22844 0.28593 -0.03730 0.14070
## seasonspring seasonsummer seasonwinter
## NA NA NAsummary(mod_type_month_year_season)##
## Call:
## lm(formula = average_price ~ type + month + year + season, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.25000 -0.18917 -0.01311 0.18043 1.49439
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.002107 0.008701 115.174 < 2e-16 ***
## typeorganic 0.500303 0.004565 109.594 < 2e-16 ***
## month10 0.290496 0.010809 26.876 < 2e-16 ***
## month11 0.171489 0.011025 15.554 < 2e-16 ***
## month12 0.036364 0.011019 3.300 0.000969 ***
## month2 -0.027110 0.011253 -2.409 0.015996 *
## month3 0.046888 0.011025 4.253 2.12e-05 ***
## month4 0.079484 0.011017 7.214 5.65e-13 ***
## month5 0.067464 0.010816 6.237 4.56e-10 ***
## month6 0.122791 0.011257 10.908 < 2e-16 ***
## month7 0.172890 0.010809 15.995 < 2e-16 ***
## month8 0.228441 0.011025 20.720 < 2e-16 ***
## month9 0.285930 0.011253 25.410 < 2e-16 ***
## year2016 -0.037298 0.005621 -6.636 3.32e-11 ***
## year2017 0.140698 0.005600 25.122 < 2e-16 ***
## seasonspring NA NA NA NA
## seasonsummer NA NA NA NA
## seasonwinter NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2972 on 16938 degrees of freedom
## Multiple R-squared: 0.4719, Adjusted R-squared: 0.4715
## F-statistic: 1081 on 14 and 16938 DF, p-value: < 2.2e-16par(mfrow = c(2, 2))
plot(mod_type_month_year_season)
1.3.5 Interactions
average_price_residual <- avocado_tidy %>%
add_residuals(mod_type_month_year_total_volume) %>%
select(-average_price)coplot(resid ~ log(total_volume) | month,
panel = function(x, y, ...){
points(x, y)
abline(lm(y ~ x), col = "blue")
},
data = average_price_residual, columns=6)
average_price_residual %>%
ggplot(aes(x = log(total_volume), y = resid, colour = type)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE)## `geom_smooth()` using formula 'y ~ x'
1.3.5.1 type - month
mod_int_t1 <- lm(average_price ~ type + month + year + total_volume + type:month, data = avocado_tidy)
summary(mod_int_t1)##
## Call:
## lm(formula = average_price ~ type + month + year + total_volume +
## type:month, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20608 -0.18751 -0.01144 0.17733 1.51395
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.010e+00 1.137e-02 88.794 < 2e-16 ***
## typeorganic 4.948e-01 1.527e-02 32.399 < 2e-16 ***
## month10 3.101e-01 1.523e-02 20.360 < 2e-16 ***
## month11 1.720e-01 1.553e-02 11.076 < 2e-16 ***
## month12 3.353e-02 1.552e-02 2.160 0.0308 *
## month2 -3.410e-02 1.585e-02 -2.151 0.0315 *
## month3 9.247e-02 1.553e-02 5.956 2.64e-09 ***
## month4 9.964e-02 1.552e-02 6.420 1.40e-10 ***
## month5 6.373e-02 1.523e-02 4.183 2.89e-05 ***
## month6 1.153e-01 1.585e-02 7.271 3.73e-13 ***
## month7 1.753e-01 1.523e-02 11.510 < 2e-16 ***
## month8 2.027e-01 1.553e-02 13.057 < 2e-16 ***
## month9 2.588e-01 1.585e-02 16.326 < 2e-16 ***
## year2016 -3.686e-02 5.600e-03 -6.582 4.76e-11 ***
## year2017 1.412e-01 5.580e-03 25.301 < 2e-16 ***
## total_volume -5.749e-09 6.923e-10 -8.305 < 2e-16 ***
## typeorganic:month10 -4.151e-02 2.154e-02 -1.927 0.0540 .
## typeorganic:month11 -3.191e-03 2.195e-02 -0.145 0.8844
## typeorganic:month12 4.502e-03 2.195e-02 0.205 0.8375
## typeorganic:month2 1.513e-02 2.242e-02 0.675 0.4997
## typeorganic:month3 -9.159e-02 2.195e-02 -4.173 3.02e-05 ***
## typeorganic:month4 -4.027e-02 2.195e-02 -1.835 0.0665 .
## typeorganic:month5 8.631e-03 2.154e-02 0.401 0.6886
## typeorganic:month6 1.572e-02 2.243e-02 0.701 0.4834
## typeorganic:month7 -5.002e-03 2.154e-02 -0.232 0.8164
## typeorganic:month8 5.065e-02 2.195e-02 2.308 0.0210 *
## typeorganic:month9 5.282e-02 2.242e-02 2.356 0.0185 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2961 on 16926 degrees of freedom
## Multiple R-squared: 0.4762, Adjusted R-squared: 0.4754
## F-statistic: 591.9 on 26 and 16926 DF, p-value: < 2.2e-161.3.5.2 month - year
mod_int_t2 <- lm(average_price ~ type + month + year + total_volume + month:year, data = avocado_tidy)
summary(mod_int_t2)##
## Call:
## lm(formula = average_price ~ type + month + year + total_volume +
## month:year, data = avocado_tidy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20897 -0.17156 -0.01063 0.16921 1.44350
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.123e+00 1.400e-02 80.230 < 2e-16 ***
## typeorganic 4.917e-01 4.527e-03 108.630 < 2e-16 ***
## month10 2.677e-02 1.950e-02 1.373 0.169853
## month11 -3.472e-02 1.850e-02 -1.877 0.060550 .
## month12 -5.950e-02 1.951e-02 -3.050 0.002294 **
## month2 -3.754e-02 1.950e-02 -1.925 0.054207 .
## month3 -2.854e-03 1.850e-02 -0.154 0.877401
## month4 1.873e-02 1.950e-02 0.961 0.336758
## month5 -1.949e-02 1.850e-02 -1.054 0.291990
## month6 3.483e-02 1.950e-02 1.786 0.074076 .
## month7 4.488e-02 1.950e-02 2.302 0.021353 *
## month8 7.965e-02 1.850e-02 4.306 1.67e-05 ***
## month9 8.424e-02 1.950e-02 4.320 1.57e-05 ***
## year2016 -1.241e-01 1.850e-02 -6.708 2.04e-11 ***
## year2017 -8.618e-02 1.850e-02 -4.659 3.21e-06 ***
## total_volume -5.437e-09 6.698e-10 -8.116 5.13e-16 ***
## month10:year2016 2.890e-01 2.616e-02 11.047 < 2e-16 ***
## month11:year2016 3.430e-01 2.616e-02 13.113 < 2e-16 ***
## month12:year2016 1.347e-01 2.689e-02 5.010 5.50e-07 ***
## month2:year2016 3.507e-02 2.688e-02 1.305 0.191959
## month3:year2016 -1.298e-02 2.616e-02 -0.496 0.619735
## month4:year2016 -5.362e-02 2.688e-02 -1.995 0.046049 *
## month5:year2016 -2.011e-02 2.542e-02 -0.791 0.429052
## month6:year2016 8.418e-03 2.688e-02 0.313 0.754129
## month7:year2016 1.162e-01 2.616e-02 4.441 9.00e-06 ***
## month8:year2016 9.115e-02 2.616e-02 3.484 0.000494 ***
## month9:year2016 1.032e-01 2.688e-02 3.840 0.000123 ***
## month10:year2017 4.465e-01 2.616e-02 17.066 < 2e-16 ***
## month11:year2017 2.732e-01 2.616e-02 10.444 < 2e-16 ***
## month12:year2017 1.451e-01 2.617e-02 5.545 2.98e-08 ***
## month2:year2017 -2.460e-02 2.688e-02 -0.915 0.359991
## month3:year2017 1.234e-01 2.616e-02 4.718 2.40e-06 ***
## month4:year2017 2.059e-01 2.616e-02 7.872 3.69e-15 ***
## month5:year2017 2.746e-01 2.616e-02 10.496 < 2e-16 ***
## month6:year2017 2.340e-01 2.689e-02 8.702 < 2e-16 ***
## month7:year2017 2.420e-01 2.616e-02 9.249 < 2e-16 ***
## month8:year2017 3.407e-01 2.616e-02 13.023 < 2e-16 ***
## month9:year2017 4.774e-01 2.688e-02 17.763 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2866 on 16915 degrees of freedom
## Multiple R-squared: 0.5097, Adjusted R-squared: 0.5086
## F-statistic: 475.2 on 37 and 16915 DF, p-value: < 2.2e-16relaimpo::calc.relimp(mod_type_month_year_total_volume, type = "lmg", rela = TRUE)## Response variable: average_price
## Total response variance: 0.1671173
## Analysis based on 16953 observations
##
## 15 Regressors:
## Some regressors combined in groups:
## Group month : month10 month11 month12 month2 month3 month4 month5 month6 month7 month8 month9
## Group year : year2016 year2017
##
## Relative importance of 4 (groups of) regressors assessed:
## month year type total_volume
##
## Proportion of variance explained by model: 47.41%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg
## month 0.13078681
## year 0.07399211
## type 0.75456058
## total_volume 0.04066050
##
## Average coefficients for different model sizes:
##
## 1group 2groups 3groups 4groups
## type 5.002927e-01 4.969983e-01 4.939747e-01 4.912087e-01
## month10 2.904960e-01 2.890097e-01 2.886308e-01 2.893588e-01
## month11 1.663762e-01 1.665884e-01 1.679718e-01 1.703928e-01
## month12 4.192540e-02 3.929673e-02 3.725483e-02 3.577504e-02
## month2 -2.957231e-02 -2.802169e-02 -2.698635e-02 -2.653008e-02
## month3 4.177503e-02 4.313927e-02 4.481640e-02 4.667318e-02
## month4 8.519383e-02 8.331178e-02 8.142483e-02 7.950803e-02
## month5 5.741402e-02 6.148067e-02 6.505841e-02 6.804710e-02
## month6 1.197779e-01 1.211728e-01 1.223033e-01 1.231046e-01
## month7 1.728902e-01 1.727509e-01 1.727154e-01 1.727836e-01
## month8 2.233277e-01 2.244754e-01 2.260974e-01 2.280602e-01
## month9 2.834678e-01 2.833520e-01 2.839625e-01 2.852349e-01
## year2016 -3.695078e-02 -3.646617e-02 -3.644299e-02 -3.685972e-02
## year2017 1.395372e-01 1.405557e-01 1.411118e-01 1.411752e-01
## total_volume -2.318360e-08 -1.739063e-08 -1.158561e-08 -5.769023e-09